Implementing Preferences with asprin

asprin offers a framework for expressing and evaluating combinations of quantitative and qualitative preferences among the stable models of a logic program. In this paper, we demonstrate the generality and flexibility of the methodology by showing how easily existing preference relations can be implemented in asprin. Moreover, we show how the computation of optimal stable models can be improved by using declarative heuristics. We empirically evaluate our contributions and contrast them with dedicated implementations. Finally, we detail key aspects of asprin’s implementation.Full Tex

Translating P-log, LPMLN, LPOD, and CR-Prolog2 into Standard Answer Set Programs

Answer set programming (ASP) is a particularly useful approach for nonmonotonic reasoning in knowledge representation. In order to handle quantitative and qualitative reasoning, a number of different extensions of ASP have been invented, such as quantitative extensions LP^{MLN} and P-log, and qualitative extensions LPOD, and CR-Prolog_2. Although each of these formalisms introduced some new and unique concepts, we present reductions of each of these languages into the standard ASP language, which not only gives us an alternative insight into the semantics of these extensions in terms of the standard ASP language, but also shows that the standard ASP is capable of representing quantitative uncertainty and qualitative uncertainty. What\u27s more, our translations yield a way to tune the semantics of LPOD and CR-Prolog_2. Since the semantics of each formalism is represented in ASP rules, we can modify their semantics by modifying the corresponding ASP rules. For future work, we plan to create a new formalism that is capable of representing quantitative and qualitative uncertainty at the same time. Since LPOD rules are simple and informative, we will first try to include quantitative preference into LPOD by adding the concept of weight and tune the semantics of LPOD by modifying the translated standard ASP rules

PREFERENCES: OPTIMIZATION, IMPORTANCE LEARNING AND STRATEGIC BEHAVIORS

Preferences are fundamental to decision making and play an important role in artificial intelligence. Our research focuses on three group of problems based on the preference formalism Answer Set Optimization (ASO): preference aggregation problems such as computing optimal (near optimal) solutions, strategic behaviors in preference representation, and learning ranks (weights) for preferences. In the first group of problems, of interest are optimal outcomes, that is, outcomes that are optimal with respect to the preorder defined by the preference rules. In this work, we consider computational problems concerning optimal outcomes. We propose, implement and study methods to compute an optimal outcome; to compute another optimal outcome once the first one is found; to compute an optimal outcome that is similar to (or, dissimilar from) a given candidate outcome; and to compute a set of optimal answer sets each significantly different from the others. For the decision version of several of these problems we establish their computational complexity. For the second topic, the strategic behaviors such as manipulation and bribery have received much attention from the social choice community. We study these concepts for preference formalisms that identify a set of optimal outcomes rather than a single winning outcome, the case common to social choice. Such preference formalisms are of interest in the context of combinatorial domains, where preference representations are only approximations to true preferences, and seeking a single optimal outcome runs a risk of missing the one which is optimal with respect to the actual preferences. In this work, we assume that preferences may be ranked (differ in importance), and we use the Pareto principle adjusted to the case of ranked preferences as the preference aggregation rule. For two important classes of preferences, representing the extreme ends of the spectrum, we provide characterizations of situations when manipulation and bribery is possible, and establish the complexity of the problem to decide that. Finally, we study the problem of learning the importance of individual preferences in preference profiles aggregated by the ranked Pareto rule or positional scoring rules. We provide a polynomial-time algorithm that finds a ranking of preferences such that the ranked profile correctly decided all the examples, whenever such a ranking exists. We also show that the problem to learn a ranking maximizing the number of correctly decided examples is NP-hard. We obtain similar results for the case of weighted profiles

Inductive learning of answer set programs

The goal of Inductive Logic Programming (ILP) is to find a hypothesis that explains a set of examples in the context of some pre-existing background knowledge. Until recently, most research on ILP targeted learning definite logic programs. This thesis constitutes the first comprehensive work on learning answer set programs, introducing new learning frameworks, theoretical results on the complexity and generality of these frameworks, algorithms for learning ASP programs, and an extensive evaluation of these algorithms. Although there is previous work on learning ASP programs, existing learning frameworks are either brave -- where examples should be explained by at least one answer set -- or cautious where examples should be explained by all answer sets. There are cases where brave induction is too weak and cautious induction is too strong. Our proposed frameworks combine brave and cautious learning and can learn ASP programs containing choice rules and constraints. Many applications of ASP use weak constraints to express a preference ordering over the answer sets of a program. Learning weak constraints corresponds to preference learning, which we achieve by introducing ordering examples. We then explore the generality of our frameworks, investigating what it means for a framework to be general enough to distinguish one hypothesis from another. We show that our frameworks are more general than both brave and cautious induction. We also present a new family of algorithms, called ILASP (Inductive Learning of Answer Set Programs), which we prove to be sound and complete. This work concerns learning from both non-noisy and noisy examples. In the latter case, ILASP returns a hypothesis that maximises the coverage of examples while minimising the length of the hypothesis. In our evaluation, we show that ILASP scales to tasks with large numbers of examples finding accurate hypotheses even in the presence of high proportions of noisy examples.Open Acces

Graph Structures for Knowledge Representation and Reasoning

This open access book constitutes the thoroughly refereed post-conference proceedings of the 6th International Workshop on Graph Structures for Knowledge Representation and Reasoning, GKR 2020, held virtually in September 2020, associated with ECAI 2020, the 24th European Conference on Artificial Intelligence. The 7 revised full papers presented together with 2 invited contributions were reviewed and selected from 9 submissions. The contributions address various issues for knowledge representation and reasoning and the common graph-theoretic background, which allows to bridge the gap between the different communities

Model-based symbolic design space exploration at the electronic system level: a systematic approach

In this thesis, a novel, fully systematic approach is proposed that addresses the automated design space exploration at the electronic system level. The problem is formulated as multi-objective optimization problem and is encoded symbolically using Answer Set Programming (ASP). Several specialized solvers are tightly coupled as background theories with the foreground ASP solver under the ASP modulo Theories (ASPmT) paradigm. By utilizing the ASPmT paradigm, the search is executed entirely systematically and the disparate synthesis steps can be coupled to explore the search space effectively.In dieser Arbeit wird ein vollständig systematischer Ansatz präsentiert, der sich mit der Entwurfsraumexploration auf der elektronischen Systemebene befasst. Das Problem wird als multikriterielles Optimierungsproblem formuliert und symbolisch mit Hilfe von Answer Set Programming (ASP) kodiert. Spezialisierte Solver sind im Rahmen des ASP modulo Theories (ASPmT) Paradigmas als Hintergrundtheorien eng mit dem ASP Solver gekoppelt. Durch die Verwendung von ASPmT wird die Suche systematisch ausgeführt und die individuellen Schritte können gekoppelt werden, um den Suchraum effektiv zu durchsuchen

Extensions of Logic Programming for Preference Representation

Εξετάζουμε το πρόβλημα της αναπαράστασης προτιμήσεων με τη χρήση επεκτάσεων του λογικού προγραμματισμού. Η αποτελεσματική αναπαράσταση προτιμήσεων είναι ζωτικής σημασίας σε πολλά επιστημονικά πεδία και μπορεί να αποδειχθεί χρήσιμη σε πολλές πραγματικές εφαρμογές. Οι φορμαλισμοί αναπαράστασης προτιμήσεων στη βιβλιογραφία συνήθως εμπίπτουν σε δύο βασικές κατηγορίες: στην ποιοτική προσέγγιση (όπου οι προτιμήσεις εκφράζονται με διμερείς σχέσεις προτίμησης) και στην ποσοτική προσέγγιση (όπου οι προτιμήσεις αναπαριστώνται με τη χρήση αριθμητικών τιμών που εκφράζουν το βαθμό ενδιαφέροντος). Σε αυτή τη διατριβή, προτείνουμε δύο προσεγγίσεις για την έκφραση προτιμήσεων. Η πρώτη προσέγγιση χρησιμοποιεί μια απειρότιμη επέκταση του λογικού προγραμματισμού για την έκφραση ποσοτικών προτιμήσεων, ενώ η δεύτερη προσέγγιση χρησιμοποιεί τον λογικό προγραμματισμό υψηλής τάξης για την έκφραση ποιοτικών προτιμήσεων. Προτείνουμε τη γλώσσα προγραμματισμού PrefLog, μια επέκταση του λογικού προγραμματισμού που χρησιμοποιεί ένα άπειρο σύνολο τιμών αλήθειας για να υποστηρίξει τον ορισμό τελεστών ποσοτικής προτίμησης. Ορίζουμε το συντακτικό και τη σημασιολογία της γλώσσας και προσδιορίζουμε ένα σύνολο από ιδιότητες τις οποίες πρέπει να ικανοποιούν οι διαθέσιμοι τελεστές προτίμησης έτσι ώστε η γλώσσα να έχει καλώς ορισμένη σημασιολογία. Επιπλέον, προτείνουμε μία «από-κάτω-προς-τα-πάνω» τεχνική υλοποίησης για ένα καλώς ορισμένο υποσύνολο της PrefLog που αντιστοιχεί στο προτιμησιακό αντίστοιχο της γλώσσας Datalog. Η εξασφάλιση της ιδιότητας του τερματισμού μιας τέτοιας στρατηγικής δεν είναι προφανής γιατί το σύνολο των τιμών αληθείας και το σύνολο των πιθανών ερμηνειών για τέτοια προγράμματα είναι και τα δύο άπειρα. Προτείνουμε τη χρήση του λογικού προγραμματισμού υψηλής τάξης για την αναπαράσταση ποιοτικών προτιμήσεων. Σε αυτήν την προσέγγιση, σχέσεις, προτιμήσεις μεταξύ πλειάδων, προτιμήσεις μεταξύ συνόλων από πλειάδες και υπολογισμοί σχετικά με προτιμήσεις εκφράζονται στην ίδια γλώσσα υψηλής τάξης. Τα προγράμματα αυτά μπορούν να εκτελεστούν σε πραγματικά συστήματα λογικού προγραμματισμού υψηλής τάξης και η απόδοσή τους μπορεί να ενισχυθεί είτε με γενικές είτε με εξειδικευμένες τεχνικές βελτιστοποίησης. Ανάμεσα σε αυτές, προτείνουμε μια νέα τεχνική μετατροπής λογικών προγραμμάτων υψηλής τάξης σε κλασικά λογικά προγράμματα (πρώτης τάξης) και την εφαρμόζουμε στα προγράμματα της προσέγγισής μας. Τέλος, αποδεικνύουμε την εφαρμοσιμότητα της προσέγγισής μας παρουσιάζοντας μια υλοποίηση και μια πειραματική αξιολόγηση στη γλώσσα λογικού προγραμματισμού υψηλής τάξης HiLog.We consider the problem of preference representation using extensions of logic programming. The effective representation of preferences is crucial in many scientific disciplines and it can be proven useful in many real-world applications. Preference representation formalisms in the literature usually fall into two basic categories: in the qualitative approach (where preferences are expressed with binary preference relations) and in the quantitative approach (where preferences are represented with the use of numerical values that express the degree of interest). In this dissertation, we propose two approaches for expressing preferences. The first approach uses an infinite-valued extension of logic programming for expressing quantitative preferences, while the second approach uses higher-order logic programming for expressing qualitative preferences. We propose PrefLog, a logic programming language which uses an underlying infinite-valued truth domain in order to support quantitative preference operators. We introduce the syntax and the semantics of the language, and we study the properties of the PrefLog operators that are needed in order for programs to behave well from a semantic point of view. In addition, we introduce a terminating bottom-up evaluation method for a well-defined class of function-free PrefLog programs. Ensuring termination is not a straightforward task, because the underlying truth domain of PrefLog and the set of all possible interpretations of a function-free PrefLog program are both infinite. We propose the use of higher-order logic programming as a framework for representing qualitative preferences. In this approach, relations, preferences between tuples, preferences between sets of tuples and operations on preferences are expressed in the same, higher-order language. The programs can be evaluated by standard higher-order programming systems, and their performance can be enhanced with generic and specialized optimization techniques. Among these techniques, we propose a novel program transformation technique for translating higher-order programs into first-order ones and we use this technique for optimizing the higher-order programs of our interest. Finally, we demonstrate the feasibility of our approach by presenting an implementation and an experimental evaluation of all the proposed concepts in the higher-order logic programming language HiLog